Magneto-elastic waves and disturbances in initially stressed conducting media

Summary The object of the present paper is to investigate magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, the theory of magneto-elastic surface waves in a conducting medium under an initial uniaxial tension has been deduced and then it has been employed to investigate the particular cases of surface waves such as Rayleigh, Love and Stoneley waves. Secondly, propagation of waves in an elastic layer has been considered using the fundamental equations of motion for magneto-elastic waves in conductors under an initial uniaxial tension or compression. This is followed by the case of plane Lamb's problem in a magneto-elastic semi-space under the same initial tension. The final results obtained in the above cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

Magneto-elastic waves in an initially stressed conducting elastic layer

Summary The paper deals with the propagation of waves in a magneto-elastic initially stressed conducting layer. The wave velocity equation obtained is in agreement with the classical result of Rayleigh and Lamb when the layer is initially unstressed and the magnetic field isabsent.     

Surface waves in magneto-elastic initially stressed conducting media

Summary The object of the present paper is to investigate the magneto-elastic surface waves in an initially stressed conducting medium. The theory of magneto-elastic surface waves in an initially stressed conducting medium has firstly been deduced and then it has been employed in investigating the particular cases of surface waves such as (i) Rayleigh waves (ii) Love waves and (iii) Stoneley waves. The wave-velocity equations obtained in different cases are in agreement with the corresponding classical results when the solid is initially unstressed and the magnetic field is absent or the material is non-magnetic.     

Onlamb's problem in a magneto-elastic initially stressed conducting medium

Summary The object of the present paper is to investigate the so-called planeLamb's problem in an initially stressed magneto-elastic semi-space bounded by a plane. The results obtained in this investigation are in agreement with the corresponding results of the classical planeLamb's problem when the semi-space is supposed to be initially unstressed and non-magnetic.     

Magneto-elastic shear waves in a conducting,infinite plate in vacuum

Summary The influence of an external magnetic field on the propagation of purely transverse waves polarized parallel to the plane faces in a homogeneous, initially unstressed, infinitely conducting, elastic flat plate extending to infinity has been investigated. We have found that such waves can be propagated only if the field is normal to the direction of polarization.The effects are of three fold depending on the inclination of the field to the direction of propagation. When the field is normal, it is to decrease the range of modes in which a disturbance of given frequency can be propagated; when parallel, it is to increase the velocity of each mode without decreasing the range of modes of propagation. In both these cases, the different modes can be classified into symmetric and anti-symmetric modes. In the general case, not only the phase velocity and the range of modes are affected over those of purely elastic case but the symmetric and anti-symmetric types of motion are coupled in every mode.     

On magneto-elastic transverse surface waves in an initially stressed half-space

Summary Transverse waves in an electrically conducting initially stressed elastic half-space with stress free boundary permeated by a magnetic field are investigated. The conditions for the existence of these waves is obtained and the velocity as well as the depth of penetration is calculated. In the absence of the initial stresses our results reduce to already known results.     

OnLamb's problem: Line load suddenly applied in a magneto-elastic initially stressed conducting half-space

Summary The paper is concerned with the investigation of the plane Lamb's problem in which a line load is suddenly applied on a magneto-elastic initially stressed conducting half-space bounded by a plane. The results obtained in this investigation are in agreement with the corresponding results of the classical plane Lamb's problem when the semispace is supposed to be initially unstressed and non-magnetic.     

Steady state response to moving loads in a magneto-elastic initially stressed conducting medium

Summary Investigated is the steady state response to moving loads in an initially stressed magneto-elastic half-space bounded by a plane. The results obtained in this problem are in agreement with the corresponding classical results when the half space is supposed to be initially unstressed and non-magnetic.     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.     

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.     

SH waves in stressed elastic plates

Summary A theoretical study is made of the propagation ofSH waves of small amplitude in an infinite elastic plate subjected to a primary normal stress. It is shown that the effect of the stress may be represented by a re-scaling of the plate thickness, provided that one elastic constant is also redefined suitably.     

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.     

Elastic waves in nonhomogeneous media under 2D conditions: II. Numerical implementation

The purpose of this work is to present three methods of analysis for elastic waves propagating in two dimensional, elastic nonhomogeneous media. The first step, common to all methods, is a transformation of the governing equations of motion so that derivatives with respect to the material parameters no longer appear in the differential operator. This procedure, however, restricts analysis to a very specific class of nonhomogeneous media, namely those for which Poisson's ratio is equal to 0.25 and the elastic parameters are quadratic functions of position. Subsequently, fundamental solutions are evaluated by: (i) conformal mapping in conjunction with wave decomposition, which in principle allows for both vertical and lateral heterogeneities; (ii) wave decomposition into pseudo-dilatational and pseudo-rotational components, which results in an Euler-type equation for the transformed solution if medium heterogeneity is a function of one coordinate only; and (iii) Fourier transformation followed by a first order differential equation system solution, where the final step involving inverse transformation from the wavenumber domain is accomplished numerically. Finally, in the companion paper numerical examples serve to illustrate the above methodologies and to delineate their range of applicability.     

Reflection and transmission of plane SH-waves in an initially stressed inhomogeneous anisotropic magnetoelastic medium

This study investigates the reflection and transmission of plane SH-waves in two semi-infinite anisotropic magnetoelastic media. The lower half-space is considered as initially stressed and inhomogeneous. The density of lower half-space is taken exponentially varying with depth. The solutions for half-spaces are obtained analytically. The expressions for reflection and transmission coefficient are obtained in the closed form subject to continuity conditions at the interfaces of anisotropic magnetoelastic half-spaces and the Snell’s law. It is found that these coefficients depend on the initial stress, inhomogeneity parameter, the magnetoelastic coupling parameter, and the angle at which wave crosses the magnetic field of the half-spaces. Numerical computations are performed for these coefficients for a specific model of two different anisotropic magnetoelastic half-spaces. The numerical results are illustrated by the graph of reflection and transmission coefficient versus the angle of incidence. In general, as the initial stress increases the reflection and transmission coefficient increases, the affect is more prominent for more than 10 GPa. Inhomogeneity in the density of the material also increases the reflection and transmission coefficient. The anisotropic magnetoelastic parameter and the angle at which the wave crosses the magnetic field for both the half-spaces have a quite significant effect on the reflection and transmission coefficient.     

Boundary shock waves in a conducting gas

Summary In this paper, we have postulated, in a conducting gas, the occurrence of a boundary shock wave, considered as a quick transition region in which the viscous effects are compressive and are confined to a thin layer adjacent to a surface. The analogues of the well known Rankine-Hugoniot jump relations, Prandtl relation, and other properties of a shock wave are derived and a discussion about the existence of a boundary shock wave is made.     

各向异性介质qP波传播描述II:分离纯模式标量波

在各向异性地震波场中,qP波与qS波常常是耦合在一起的.多分量地震数据处理中一个关键环节就是波型分离(即模式解耦),以纵波成分为主的常规单分量地震数据的成像则需要合理描述标量qP波的传播算子.本文作者曾构建了在运动学上同弹性波动方程等价,动力学上突出标量qP波的伪纯模式波动方程.为了彻底消除qS波残余,本文根据波矢量与qP波偏振矢量之间的偏差,提出从伪纯模式波场提取纯模式标量qP波的方法.数值分析展示了投影偏差算子在波数域和空间域的特征.基于不同复杂程度理论模型的试验结果表明,联合"伪纯模式传播算子"与"投影偏差校正"可为各向异性介质分离模式波场传播过程提供一种简便的描述工具.     

Thermoelastic waves in non-simple media

Summary The present paper is an attempt to investigate the propagation of thermoelastic waves propagated in non-simple media and study the distinction between propagation in simple and nonsimple media. Plane progressive waves and Rayleigh waves have been discussed.     

On love waves in heterogeneous media

Summary Love waves in a half space with one homogeneous elastic layer overlying a semiinfinite medium having elastic properties varying with depth has been considered. The frequency equation for small wave lengths has been obtained, considering general variation, and has been shown to involve the first three derivatives of the rigidity of the heterogeneous medium at its interface with the homogeneous layer.     

Surface and plate waves in biaxially-stressed elastic media

Summary The propagation of waves of small amplitude in an incompressible elastic medium subjected to a large homogeneous equibiaxial stress is investigated. The dispersion equation for surface waves on a semi-infinite medium is obtained explicitly, and the dispersion equation for waves in a slab of finite depth. In the latter case, approximate values, valid for waves whose lengths are much greater than the slab thickness, are determined for the phase-velocities of the different modes.